Values of the log-posterior

Hi all,

I have a general question regarding STAN-Sampling.

When sampling from a univariate normal distribution, I obtain MCMC-samples x_1,...,x_R from which I can obtain the logposterior-value. Plotting the histogram of these leads to the following plot (like the lp__-Histogram in the pairs plot). This makes sense to me: Most of the samples lie where the density is the highest.


However, when looking at a general example model, the histogram of the log-posterior has a very different form, more like a bell-shape. It seems like a lot less samples lie in regions with a high density value (>-110) and most samples lie in regions with density values around -115. Why is that the case?

In my specific example, the posterior has two modes and I plot the histograms of the sampled lp-values for both modes separately. Here again, I have bellshaped curves. However, I conclude that the mode corresponding to the grey histogram is the higher and hence desirable mode. Is that correct?


Thank you for your thoughts,

because the region of high likelihood is comparably quite small.